Controlled herd immunity as you say appears to be the way forward - but why the Government havent already started nationwide blood testing of the population I'll never know.
Every GP service/walk in should be giving people 5 minute appointments to have a blood sample taken - if someone turns up early have them que up like at the supermarkets and have the people performing the tests kitted out in proper PPE.
Anyone who tests positive for antibodies - add them to a nation wide database and after so many weeks you have an idea of what stage we are at in terms of relaxing the lockdown and if we need to shut back up again once cases spike then do so.
Without testing we are peeing against the wind.
I think its important to be clear and distinguish on herd immunity. Herd immunity as a cincept has gotten a bit confused since the term was trotted out and became a political approach - like early in the Uk reaction - or running straight into natural herd immunity like Sweden.
There are two ways herd immunity is achieved:
1) Natural - catching the virus and developing immunity.
2) Artificial - having a vaccine.
A reasonable approach is to accept, that people are going to catch the virus and natural herd immunity will slowly progress, but recognising if you purposely try to develop, your health service will be swamped and yu will have a lot of deaths on your hands.
If you can control the natural herd immunity growth rate, through hammer and dance approach, you grow natural herd immunity incrementally, while trying to preserve and save lives. In the back ground you are buying time for a vaccine to developed and artificial herd immunity achieved. Both sides of the herd immunity are essentially eeking together to provide protection and reduce risk. Essentially all decisions in managing this are about managing the time until a vaccine can be developed in the best way that saves lives.
I think its unlikely we will achieve a minimum of 60% natural herd immunity before a vaccine artificial herd immunity.
So a question on anti body testing is, are precious resources better spent on developing testing those who may have the virus now, tracing their contacts and identifying clusters or are they best spent on those who may/may not already have immunity and what purpose would that serve. Id go for the first option myself.